The two legs of a right triangle are the same length. The hypotenuse is 4 meters long.
Find the length of the legs. Express your answer in simplified radical form, or as a decimal rounded to four places.
Solution
Let x be the length of one leg and let x be the length of the other leg.
x^{2} + x^{2} = 4^{2}
2x^{2} = 16
Divide both sides by 2
x^{2} = 8
x = √(8)
x = √(4 × 2)
x = √(4) × √(2)
x = 2 × √(2)
or
x = 2 × 1.414213
x = 2.828426
x = 2.8284
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